Solve the trigonometric equation in the interval ( 0 , 2 π ] \left(0,\ 2\pi\right] ( 0 , 2 π ] . 11 sin ⁡ x + 5 = sin ⁡ x 11\sin x+5=\sin x 1 1 sin x + 5 = sin x

7 π 6 , 11 π 6 \frac{7\pi}{6},\frac{11\pi}{6} 6 7 π , 6 1 1 π

π 3 , 2 π 3 \frac{\pi}{3},\frac{2\pi}{3} 3 π , 3 2 π

π 6 , 5 π 6 \frac{\pi}{6},\frac{5\pi}{6} 6 π , 6 5 π

π 6 , 5 π 6 , 7 π 6 , 11 π 6 \frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6} 6 π , 6 5 π , 6 7 π , 6 1 1 π

Solve the trigonometric equation in the interval ( 0 , 2 π ] \left(0,\ 2\pi\right] ( 0 , 2 π ] . 2 sin ⁡ 3 x + 3 = 0 2\sin3x+\sqrt{3}=0 2 sin 3 x + 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> = 0

4 π 9 , 5 π 9 \frac{4\pi}{9},\frac{5\pi}{9} 9 4 π , 9 5 π

π 2 , 2 π 3 \frac{\pi}{2},\frac{2\pi}{3} 2 π , 3 2 π

4 π 3 , 5 π 3 \frac{4\pi}{3},\frac{5\pi}{3} 3 4 π , 3 5 π

π 6 , 4 π 9 , 2 π 9 , 5 π 9 \frac{\pi}{6},\frac{4\pi}{9},\frac{2\pi}{9},\frac{5\pi}{9} 6 π , 9 4 π , 9 2 π , 9 5 π

Given x : [0, 2 π], Solve the following equation: cos ⁡ x = 1 2 \cos\ x\ =\frac{1}{2} cos x = 2 1

x = π 3 , 5 π 3 x\ =\ \frac{\pi}{3}\ \ ,\ \ \frac{5\pi}{3} x = 3 π , 3 5 π

x = π 3 , 2 π 3 x\ =\ \frac{\pi}{3}\ \ ,\ \ \frac{2\pi}{3} x = 3 π , 3 2 π

x = 4 π 3 , 5 π 3 x\ =\ \frac{4\pi}{3}\ \ ,\ \ \frac{5\pi}{3} x = 3 4 π , 3 5 π

x = π 3 , π 2 x\ =\ \frac{\pi}{3}\ \ ,\ \ \frac{\pi}{2} x = 3 π , 2 π

Given x : [0, 2 π], Solve the following equation: cos ⁡ x = 0 \cos\ x\ =0 cos x = 0

x = π 2 , 3 π 2 x\ =\ \frac{\pi}{2}\ \ ,\ \frac{3\pi}{2} x = 2 π , 2 3 π

x = 0 , π , 2 π x\ =\ 0\ ,\ \pi\ ,\ 2\pi x = 0 , π , 2 π

x = π , 2 π x\ =\pi\ ,\ \ 2\pi x = π , 2 π

x = π 2 x\ =\ \frac{\pi}{2}\ \ x = 2 π

x = 3 π 2 x\ =\ \frac{3\pi}{2} x = 2 3 π

Given x : [0, 2 π], Solve the following equation: sin ⁡ x = 0 \sin\ x\ =0 sin x = 0

x = 0 , π , 2 π x\ =\ 0\ ,\ \pi\ ,\ 2\pi x = 0 , π , 2 π

x = π 2 o r 3 π 2 x\ =\ \frac{\pi}{2}\ \ or\ \ \frac{3\pi}{2} x = 2 π o r 2 3 π

x = π , 2 π x\ =\pi\ ,\ \ 2\pi x = π , 2 π

x = π 2 x\ =\ \frac{\pi}{2}\ \ x = 2 π

x = 3 π 2 x\ =\ \frac{3\pi}{2} x = 2 3 π

Given x : [0, 2 π], Solve the following equation: sin ⁡ x = − 3 2 \sin\ x\ =-\frac{\sqrt{3}}{2} sin x = − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

x = 4 π 3 , 5 π 3 x\ =\ \frac{4\pi}{3}\ ,\ \ \ \frac{5\pi}{3} x = 3 4 π , 3 5 π

x = π 3 , 2 π 3 x\ =\ \frac{\pi}{3}\ ,\ \ \frac{2\pi}{3} x = 3 π , 3 2 π

x = 4 π 3 , π 3 x\ =\ \frac{4\pi}{3}\ ,\ \ \frac{\pi}{3} x = 3 4 π , 3 π

x = 2 π 3 , 5 π 3 x\ =\ \frac{2\pi}{3}\ \ ,\ \frac{5\pi}{3} x = 3 2 π , 3 5 π

x = 2 π 3 , 4 π 3 x\ =\ \frac{2\pi}{3}\ ,\ \ \ \frac{4\pi}{3} x = 3 2 π , 3 4 π

Given x : [0, 2 π], Solve the following equation: sin ⁡ x = − 1 \sin\ x\ =-1 sin x = − 1

x = 3 π 2 x\ =\ \frac{3\pi}{2} x = 2 3 π

x = π 2 o r 3 π 2 x\ =\ \frac{\pi}{2}\ \ or\ \ \frac{3\pi}{2} x = 2 π o r 2 3 π

x = 0 , π , 2 π x\ =\ 0\ ,\ \pi\ ,\ 2\pi x = 0 , π , 2 π

x = π , 2 π x\ =\pi\ ,\ \ 2\pi x = π , 2 π

x = π 2 x\ =\ \frac{\pi}{2}\ \ x = 2 π

Given x : [0, 2 π], Solve the following equation: 12 cos ⁡ x + 6 √ 3 = 0 12\cos x+6√3=0 1 2 cos x + 6 √ 3 = 0

x = 7 π 6 , 5 π 6 x\ =\ \frac{7\pi}{6}\ \ ,\ \ \ \frac{5\pi}{6} x = 6 7 π , 6 5 π

x = 5 π 6 , 11 π 6 x\ =\ \frac{5\pi}{6}\ \ ,\ \ \ \frac{11\pi}{6} x = 6 5 π , 6 1 1 π

x = π 6 , 5 π 6 x\ =\ \frac{\pi}{6}\ \ ,\ \ \ \frac{5\pi}{6} x = 6 π , 6 5 π

x = 7 π 6 , π 6 x\ =\ \frac{7\pi}{6}\ \ ,\ \ \ \frac{\pi}{6} x = 6 7 π , 6 π

x = π 6 , 11 π 6 x\ =\ \frac{\pi}{6}\ \ ,\ \ \ \frac{11\pi}{6} x = 6 π , 6 1 1 π

Given x : [0, 2 π], Solve the following equation: 8 sin ⁡ x + 4 = 0 8\sin x+4=0 8 sin x + 4 = 0

x = 7 π 6 , 11 π 6 x\ =\ \frac{7\pi}{6}\ \ ,\ \ \ \frac{11\pi}{6} x = 6 7 π , 6 1 1 π

x = 5 π 6 , 11 π 6 x\ =\ \frac{5\pi}{6}\ \ ,\ \ \ \frac{11\pi}{6} x = 6 5 π , 6 1 1 π

x = π 6 , 5 π 6 x\ =\ \frac{\pi}{6}\ \ ,\ \ \ \frac{5\pi}{6} x = 6 π , 6 5 π

x = 11 π 6 , π 6 x\ =\ \frac{11\pi}{6}\ \ ,\ \ \ \frac{\pi}{6} x = 6 1 1 π , 6 π

x = 7 π 6 , 5 π 6 x\ =\ \frac{7\pi}{6}\ \ ,\ \ \ \frac{5\pi}{6} x = 6 7 π , 6 5 π

Given x : [0, 2 π], Solve the following equation: − 10 cos ⁡ x + 6 = 1 -10\cos x+6=1 − 1 0 cos x + 6 = 1

x = π 3 , 5 π 3 x\ =\ \frac{\pi}{3}\ \ ,\ \ \frac{5\pi}{3} x = 3 π , 3 5 π

x = 4 π 3 , 5 π 3 x\ =\ \frac{4\pi}{3}\ ,\ \ \ \frac{5\pi}{3} x = 3 4 π , 3 5 π

x = π 3 , 2 π 3 x\ =\ \frac{\pi}{3}\ ,\ \ \frac{2\pi}{3} x = 3 π , 3 2 π

x = 4 π 3 , π 3 x\ =\ \frac{4\pi}{3}\ ,\ \ \frac{\pi}{3} x = 3 4 π , 3 π

x = 2 π 3 , 4 π 3 x\ =\ \frac{2\pi}{3}\ ,\ \ \ \frac{4\pi}{3} x = 3 2 π , 3 4 π

Given x : [0, 2 π], Solve the following equation: 14 sin ⁡ x + 7 2 = 0 14\sin x+7\sqrt{2}=0 1 4 sin x + 7 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> = 0

x = 5 π 4 , 7 π 4 x\ =\ \frac{5\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4} x = 4 5 π , 4 7 π

x = π 4 , 7 π 4 x\ =\ \frac{\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4} x = 4 π , 4 7 π

x = 5 π 4 , 3 π 4 x\ =\ \frac{5\pi}{4}\ \ ,\ \ \ \frac{3\pi}{4} x = 4 5 π , 4 3 π

x = 3 π 4 , 7 π 4 x\ =\ \frac{3\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4} x = 4 3 π , 4 7 π

x = 5 π 4 , π 4 x\ =\ \frac{5\pi}{4}\ \ ,\ \ \ \frac{\pi}{4} x = 4 5 π , 4 π

Given x : [0, 2 π], Solve the following equation: − 16 sin ⁡ x + 8 2 = 0 -16\sin x+8\sqrt{2}=0 − 1 6 sin x + 8 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> = 0

x = 3 π 4 , π 4 x\ =\ \frac{3\pi}{4}\ \ ,\ \ \ \frac{\pi}{4} x = 4 3 π , 4 π

x = 5 π 4 , 7 π 4 x\ =\ \frac{5\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4} x = 4 5 π , 4 7 π

x = π 4 , 7 π 4 x\ =\ \frac{\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4} x = 4 π , 4 7 π

x = 5 π 4 , 3 π 4 x\ =\ \frac{5\pi}{4}\ \ ,\ \ \ \frac{3\pi}{4} x = 4 5 π , 4 3 π

x = 3 π 4 , 7 π 4 x\ =\ \frac{3\pi}{4}\ \ ,\ \ \ \frac{7\pi}{4} x = 4 3 π , 4 7 π

Given x : [0, 2 π], Solve the following equation: 5 cos ⁡ x + 2 = − 3 5\cos x\ +2=-3 5 cos x + 2 = − 3

x = π 2 o r 3 π 2 x\ =\ \frac{\pi}{2}\ \ or\ \ \frac{3\pi}{2} x = 2 π o r 2 3 π

x = 0 , π , 2 π x\ =\ 0\ ,\ \pi\ ,\ 2\pi x = 0 , π , 2 π

x = π 2 x\ =\ \frac{\pi}{2}\ \ x = 2 π

x = 3 π 2 x\ =\ \frac{3\pi}{2} x = 2 3 π

Given x : [0, 2 π], Solve the following equation: 5 sin ⁡ x − 2 = 3 5\sin x\ -2=3 5 sin x − 2 = 3

x = π 2 x\ =\ \frac{\pi}{2}\ \ x = 2 π

x = π 2 o r 3 π 2 x\ =\ \frac{\pi}{2}\ \ or\ \ \frac{3\pi}{2} x = 2 π o r 2 3 π

x = 0 , π , 2 π x\ =\ 0\ ,\ \pi\ ,\ 2\pi x = 0 , π , 2 π

x = π , 2 π x\ =\pi\ ,\ \ 2\pi x = π , 2 π

x = 3 π 2 x\ =\ \frac{3\pi}{2} x = 2 3 π

Absent 3/21/25 Quiz

25 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Solve on the domain [0,2π)
cos x + 1 = 0

0

No solution

π

3π/2

Tags

CCSS.HSF.TF.B.7

2.

MULTIPLE CHOICE QUESTION

5 mins • 2 pts

A

B

C

D

Tags

CCSS.HSF.TF.B.7

3.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Solve for 0≤x≤2π

4cos²x- 2 = 0

π/3, 5π/3

π/4, 7π/4

3π/4, 5π/4

π/6, 11π/6

Tags

CCSS.HSF.TF.B.7

4.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

A

B

C

D

Tags

CCSS.HSF.TF.B.7

5.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Tags

CCSS.HSF.TF.B.7

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Tags

CCSS.HSF.TF.B.7

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$11\sin x+5=\sin x$

$\frac{\pi}{3},\frac{2\pi}{3}$

$\frac{\pi}{6},\frac{5\pi}{6}$

$\frac{7\pi}{6},\frac{11\pi}{6}$

$\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

Tags

CCSS.HSF.TF.B.7

8.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$2\sin3x+\sqrt{3}=0$

$\frac{\pi}{2},\frac{2\pi}{3}$

$\frac{4\pi}{3},\frac{5\pi}{3}$

$\frac{4\pi}{9},\frac{5\pi}{9}$

$\frac{\pi}{6},\frac{4\pi}{9},\frac{2\pi}{9},\frac{5\pi}{9}$

Tags

CCSS.HSF.TF.B.7

9.

MULTIPLE SELECT QUESTION

45 sec • 1 pt

Which of the following are the correct solutions for the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ ?

CHOOSE ALL THAT APPLY

$\cos x=0$

$\frac{3\pi}{2}$

$\pi$

$2\pi$

$\frac{\pi}{2}$

Tags

CCSS.HSF.TF.B.7

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Absent 3/21/25

Solve on the domain [0,2π)cos x + 1 = 0

Solve for 0≤x≤2π4cos2x - 2 = 0

Solve the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] . 11sin⁡x+5=sin⁡x11\sin x+5=\sin x11sinx+5=sinx

Solve the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] . 2sin⁡3x+3=02\sin3x+\sqrt{3}=02sin3x+3​=0

Which of the following are the correct solutions for the trigonometric equation in the interval (0, 2π]\left(0,\ 2\pi\right](0, 2π] ? CHOOSE ALL THAT APPLY cos⁡x=0\cos x=0cosx=0

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Discover more resources for Mathematics

Solve on the domain [0,2π)
cos x + 1 = 0

Solve for 0≤x≤2π

4cos²x- 2 = 0

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$11\sin x+5=\sin x$

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$2\sin3x+\sqrt{3}=0$

Which of the following are the correct solutions for the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ ?

CHOOSE ALL THAT APPLY

$\cos x=0$